SPY/GLD/TLT optimized portfolio balance

[BinaryAlgorithm]

Ran tests from 2005-present using daily historical data. Initially I used the Excel solver with a max drawdown setting of 20% and then 15%, telling it to maximize returns. Then I had it minimize drawdown (it was able to reach a low of 13.7%). The highest ratio of annualized return divided by max drawdown is produced with about a 20/20/60 portfolio split:

Of course, this is a static portfolio. I coded a dynamic portfolio strategy in C# using the same data and then ran every allocation of the 3 assets with a 5% step (like 25/35/40, etc). If an asset was 3% over its target allocation some was sold and invested into the others to rebalance. Here is the 20/20/60:

The best dynamic strategy is actually 25/20/55 with a 8.22% annualized return and 12.9% max drawdown (so it outperforms the static portfolio - the return is almost as good as 100% SPY but the % max drawdown is less than 1/4 - positive alpha!).

So that is a solid foundation. Now, I want to 2-3x leverage that. The harder part is doing the allocations right for options or futures.

Options:

SPY, GLD, and TLT all have Jan 2022 call options with a 1.00 delta. The idea is to roll annually so that DTE is always between 1-2 years. I *think* what I'd want to do to more or less replicate the results above is to have total delta be about a 1:1:3 ratio (is that right?). The other method is to have 1:1:3 leverage ratios. I'm not exactly sure.

Futures:

ES/GC/ZB mix should replicate the behavior. I am not rich so I guess MES/MGC/ZB since I don't plan to use FOPs, in which case the closest I can get is 3:3:1 (treasury has no micro so 1 ZB really makes this like 3:3:10). That is around 250k of assets on a 40k account, and periodic rebalancing like I did with the ETFs is not possible here unless there is a huge move in relative prices. The margin might be only about 3500, but that's already at 6x leverage compared to using ETFs (dangerous even with a max drawdown of 13-15%). Is that a comparable asset balance in terms of % movements? Based on spreads/liquidity, it looks like rolling every 3 months would be the plan for this one.

Summary:

If I want to maintain a dynamic allocation of about 20/20/60, what are the pros/cons of:

(1) Borrow the ETFs on margin (about 3.4% rate currently), to a leverage level of 1.5-1.7. With the expected max drawdown (say 15%) of the portfolio, it is still possible to dynamically rebalance within Reg T margin.

(2) Use call options with some ratio that replicates the desired portfolio balance.

(3) Use futures to replicate the desired portfolio balance.

And for 2 and 3, how would I balance it properly?

 

[Magic]

Borrow on margin and slowly slide futures in as capital permits.

And I'm all for levering a more efficient portfolio, but I wouldn't go so far as to call it alpha. Choosing allocation by copying the best performing assets in the most recent block of time is going to likely lead to under-performance. Markets are cyclical. If you dig up older data, solve for the best allocation from something like 1935 - 1950 and then run it forward a decade from there that will probably be a more realistic picture of what you're trying to do.

By the time you account for tax drag, cost of borrowing, and extra commissions from frequent re-balancing the edge will end up being a lot thinner than you think. Definitely think you're on the start of a good path here though. Taking the jump from following dogma to working with the actual data is a great step to take as an investor.

 

[traider]

Borrow on margin and slowly slide futures in as capital permits.

And I'm all for levering a more efficient portfolio, but I wouldn't go so far as to call it alpha. Choosing allocation by copying the best performing assets in the most recent block of time is going to likely lead to under-performance. Markets are cyclical. If you dig up older data, solve for the best allocation from something like 1935 - 1950 and then run it forward a decade from there that will probably be a more realistic picture of what you're trying to do.

By the time you account for tax drag, cost of borrowing, and extra commissions from frequent re-balancing the edge will end up being a lot thinner than you think. Definitely think you're on the start of a good path here though. Taking the jump from following dogma to working with the actual data is a great step to take as an investor.

Then please show us what is true alpha

 

[Magic]

First and foremost alpha is a syntax debate lol.

But imo alpha source is something that gives a significantly superior return profile vs. an easily replicated benchmark. And when enough people know about an alpha source it's eroded into a realistic risk premium for the risk factors associated with it, i.e. beta.

Private models or systemic trading logic that can't be easily copied by other alpha-seekers are more what I'm talking about. For example here's my best strategy quarter-to-date; I don't even know if I'd consider this pure alpha.. but stats like these are getting a little closer to the mark.

 

[TommyR]

this is in my opinion what true alpha looks like. it never worries if it's losing it's edge. it doesn't have off days or start going down randomly

 

[R1234]

Ran tests from 2005-present using daily historical data. Initially I used the Excel solver with a max drawdown setting of 20% and then 15%, telling it to maximize returns. Then I had it minimize drawdown (it was able to reach a low of 13.7%). The highest ratio of annualized return divided by max drawdown is produced with about a 20/20/60 portfolio split:

View attachment 215116

Of course, this is a static portfolio. I coded a dynamic portfolio strategy in C# using the same data and then ran every allocation of the 3 assets with a 5% step (like 25/35/40, etc). If an asset was 3% over its target allocation some was sold and invested into the others to rebalance. Here is the 20/20/60:

View attachment 215119

The best dynamic strategy is actually 25/20/55 with a 8.22% annualized return and 12.9% max drawdown (so it outperforms the static portfolio - the return is almost as good as 100% SPY but the % max drawdown is less than 1/4 - positive alpha!).

So that is a solid foundation. Now, I want to 2-3x leverage that. The harder part is doing the allocations right for options or futures.

Options:

SPY, GLD, and TLT all have Jan 2022 call options with a 1.00 delta. The idea is to roll annually so that DTE is always between 1-2 years. I *think* what I'd want to do to more or less replicate the results above is to have total delta be about a 1:1:3 ratio (is that right?). The other method is to have 1:1:3 leverage ratios. I'm not exactly sure.

Futures:

ES/GC/ZB mix should replicate the behavior. I am not rich so I guess MES/MGC/ZB since I don't plan to use FOPs, in which case the closest I can get is 3:3:1 (treasury has no micro so 1 ZB really makes this like 3:3:10). That is around 250k of assets on a 40k account, and periodic rebalancing like I did with the ETFs is not possible here unless there is a huge move in relative prices. The margin might be only about 3500, but that's already at 6x leverage compared to using ETFs (dangerous even with a max drawdown of 13-15%). Is that a comparable asset balance in terms of % movements? Based on spreads/liquidity, it looks like rolling every 3 months would be the plan for this one.

Summary:

If I want to maintain a dynamic allocation of about 20/20/60, what are the pros/cons of:

(1) Borrow the ETFs on margin (about 3.4% rate currently), to a leverage level of 1.5-1.7. With the expected max drawdown (say 15%) of the portfolio, it is still possible to dynamically rebalance within Reg T margin.

(2) Use call options with some ratio that replicates the desired portfolio balance.

(3) Use futures to replicate the desired portfolio balance.

And for 2 and 3, how would I balance it properly?

In the futures version you could replace ZB with ZF. It behaves like sort of a mini ZB because of the smaller duration and the notional value is around 120k per contract.

 

[Daal]

I have run backtests similar to yours going back from 1926 to 2017 on US data, as well as UK data going back a century plus Greece and Brazil data for tail event testing. What I discovered is that 'balance' is achieved by building a Taleb like 'barbell portfolio'. You have arrived at the same conclusion, you are just not seeing it. A 20% stock 20% gold and 60% bond portfolio is a taleb barbell, bonds 'mixed' with gold are a very stable store of value while stocks are a high return high drawdown asset. At that 80/20 balance (80% bonds/gold balanced at a 3-1 or 4-1 ratio) with 20% stocks tend to achieve higher risk adjusted returns than other portfolios. Although I my own testing I recalled achieving better performance (measured by Sortino, Gain to Pain and other metrics) with higher stock allocations.

As far as leverage is concerned, its a tricky thing because it carries massive tail risks. In a Greek scenario a 2-1 leverage leads to a blow up quite fast (stocks went down 95%+ and bonds -70%, 20% gold was not enough to save the day), Brazil also had periods like that. But one could say 'The US is not like those countries, its safe to lever up here' (that is what Ray Dalio thinks and what he does in his All-Weather hedge fund), maybe, or maybe not. Even in the UK in the 70's the drawdowns that a highly levered portfolio would have that were huge (bonds and stocks collapsed massively, the pound also went down huge).
In my view, if you want to lever up like that consider doing the following
-Using a GLOBAL portfolio instead of a US centric one. So global stocks, global bonds and gold
-Limit leverage to 1.3/1.4, both to cut down tail risks and for sanity purposes. higher leverage ONLY make sense AFTER markets are down massively (2009), after a decade of a bull market it aint the time to be thinking of levering up assets
-Use whatever instrument minimize taxes and transaction costs, whether its futures/options/margin debt it will depend on your specific situation

 

[BinaryAlgorithm]

One reason I didn't care to calculate alpha. For my purposes (margin, safe leverage, etc), max drawdown is more relevant. Yes, a straight line with no drawdown is pure alpha, and you could leverage the crap out of that (if it persists of course).

I got started on this when looking at asset correlation matrices - there's a limited number of really distinct asset categories that actually help. Stock + bond improves the risk profile as is well-known, but from my testing stock + bond + gold improved it more. Adding additional ETFs, I couldn't really find a 4th one that further improved things; most things that look like alternatives just become more correlated to SPY when it drops significantly.

At the start of the study, the relative prices put the share ratios at 17.7%/26.7%/55.6%. If I put 20/20/60 in value terms, I get (at current prices) 9.8%/22.4%/67.8% in terms of number of shares of the ETFs. SPY is (relatively) more expensive right now. Not sure if it matters though in the long run. The rebalancing idea essentially causes me to sell when one asset (relative to the others) gains a lot of value, and buy when it loses value, so there is some cyclical timing aspect which is build into the strategy which improves it. Selling at 3% above target allocation worked better than 5% and doesn't trigger that often, but I didn't go lower because the improvement is very small and I didn't factor in transaction costs (it is only useful to go smaller and rebalance more frequently if the adjustments are at least 100 share blocks in a large portfolio; I was using 10 for a 100k test portfolio; the 'improvement' of rebalancing as you go toward continuous rebalancing is probably just curve-fitting anyway).

If I use options, I found that I can make it uniform with 1.00 delta contracts all with about 2.2x leverage so that the relative price changes should remain similar to the stock based concept. I get the same relative number of options in that case as I do with the ETF shares. The carry cost is neutralized for SPY and TLT these because they pay dividends higher than the normal interest carry cost, whereas GLD has a carry cost of about 3.5% for 2 year LEAPs but it is only 20% of the portfolio so the overall options roll and carry cost is not bad; I would let them expire and repurchase immediately rather than doing an actual calendar roll to save on spread costs.

If I do options or futures I won't get the improvement from rebalancing most likely because the threshold to do even 1 contract is a significant percentage change off the target (starting with 40k for 25/57/173 shares doesn't really allow for it, though I am adding about 2000/mo). So, the result is more likely to be similar to my test result when I exclude rebalancing. It's still good enough without that component to want to apply leverage, but it's hard to get the target ratios in the first place.

The main advantage of the ETFs is the rebalancing granularity on a smaller account: you can do 10 shares easily (probably the minimum I'd balance it by) and yeah it's a dollar minimum commission at IB but it doesn't need to rebalance that often and you can be a bit looser with that without affecting the outcome too much - it only really matters to adjust after large relative movements, more than exactly when, so you don't have to be too mechanical about it. I can use a bit of regular margin to enhance the result.

 

[Daal]

Fun fact: The worse time for portfolios like this in the US were not in the 1930's, 1970's or 2008 if you can believe that. It was in the 1940's. That was when the optimal portfolios had its worse max real drawdown. It happened because of inflation was hurting stocks and bonds, meanwhile the gold price was FIXED. The net result was a -26% real drawdown to a 30% stocks, 55% bond and 15% gold 'optimal' allocation (annual re-balancing)

 

[BinaryAlgorithm]

I have run backtests similar to yours going back from 1926 to 2017 on US data, as well as UK data going back a century plus Greece and Brazil data for tail event testing. What I discovered is that 'balance' is achieved by building a Taleb like 'barbell portfolio'. You have arrived at the same conclusion, you are just not seeing it. A 20% stock 20% gold and 60% bond portfolio is a taleb barbell, bonds 'mixed' with gold are a very stable store of value while stocks are a high return high drawdown asset. At that 80/20 balance (80% bonds/gold balanced at a 3-1 or 4-1 ratio) with 20% stocks tend to achieve higher risk adjusted returns than other portfolios. Although I my own testing I recalled achieving better performance (measured by Sortino, Gain to Pain and other metrics) with higher stock allocations.

As far as leverage is concerned, its a tricky thing because it carries massive tail risks. In a Greek scenario a 2-1 leverage leads to a blow up quite fast (stocks went down 95%+ and bonds -70%, 20% gold was not enough to save the day), Brazil also had periods like that. But one could say 'The US is not like those countries, its safe to lever up here' (that is what Ray Dalio thinks and what he does in his All-Weather hedge fund), maybe, or maybe not. Even in the UK in the 70's the drawdowns that a highly levered portfolio would have that were huge (bonds and stocks collapsed massively, the pound also went down huge).
In my view, if you want to lever up like that consider doing the following
-Using a GLOBAL portfolio instead of a US centric one. So global stocks, global bonds and gold
-Limit leverage to 1.3/1.4, both to cut down tail risks and for sanity purposes. higher leverage ONLY make sense AFTER markets are down massively (2009), after a decade of a bull market it aint the time to be thinking of levering up assets
-Use whatever instrument minimize taxes and transaction costs, whether its futures/options/margin debt it will depend on your specific situation

Good info to keep in mind. Yeah, this exponential debt / rate suppression regime will probably last for awhile yet and it's what's really driving the prices up in this study, but it could change. I've researched the "debt super cycle" and I am a bit afraid how it will conclude, but other than creating more monetary units to soft default what can all these countries do?

Do you happen to know good ETFs for global exposure? I am not familiar but from what I understand equities in general will behave the same way for portfolio purposes; it provides at least some diversification value (in the equities component). US appears to be the better of the bunch, but not if we keep being irresponsible, so I get what you are saying. However, when it blows it's probably going to be global anyway...

I'm still in the 12% tax bracket and I get certain write-offs such that I'm not (yet) concerned with tax impact. I can thus realize gains each year from rebalancing the portfolio as opposed to trying to defer unrealized gains. I'll worry about it when it becomes more significant.

Yes, in some tests I can run 25-30% stock instead of 20% and it does well; diversified global index may make the difference and also you ran longer time frames so I'll consider that (I didn't have data back that far since I was using ETF history).

So, any reasons you would recommend ETF, ETF options (I can't get less than 2x leverage on TLT so I just kind of standardized them all to 2.2x in my testing; you get optionality in a crash but it won't really save you), or futures as the vehicle?